1. Field of the Invention
The present invention is directed to an X-ray imaging system of the type wherein an X-ray radiator and a radiation receiver are mounted on a holding device and are rotated around a measuring field, in which an examination subject is disposed, for transirradiating the measuring field from different directions, and wherein an image of the examination subject is produced in a computer from the images obtained from the different directions.
2. Description of the Prior Art
There are known X-ray imaging systems in which an image receiver is provided, e.g. from a matrix of detector elements on the basis of amorphous, hydrogenated silicon, or an X-ray image intensifier is provided which is struck by a pyramid-shaped X-ray beam bundle, an X-ray image being created from the output signals of this intensifier with the aid of a computer. One such system is, for example, a C-arm apparatus with an X-ray source at the one end and a surface detector at the other end of a C-arm. Such X-ray imaging systems are mechanically unstable, given motion of the C-arm; i.e., the radiation geometry can change due to slight displacements of the focus or the detector. On the other hand, the open structure guarantees a good patient accessibility; i.e., the system is also suitable for use during an interventional procedure. In order to construct qualitatively good images with high spatial resolution, in known reconstruction algorithms the respective position of the focus and the detector relative to a fixed spatial coordinates system must be detected in a measurement conducted in the same fashion as the (subsequent) patient examination, and entered into the reconstruction algorithm. This occurs in a back projection, which can be realized either as a software solution on a general-purpose computer or with special hardware.
The focus in a computer tomography apparatus describes a perfect orbit about the isocenter without mechanical instabilities. The axis perpendicular to the plane of the circle through the isocenter is called the axis of rotation of the system. The detector is located at a constant distance. The detection surface is thus always perpendicular to the center beam which travels from the focus through the isocenter (optical axis).
For this type of reception geometry, an algorithm which consists essentially of a row-by-row preprocessing (convolution) and a back projection is described in L. A. Feldkamp, L. C. Davis, and J. W. Kre.beta., "Practical Cone-Beam Algorithm"; J. Opt. Soc. Amer. A, Vol. 1, No. 6, pp 612-619, 1984.
If a C-arm device is used, two substantial deviations from this ideal geometry arise which force a modification of the Feldkamp Algorithm:
1. Partial revolution; i.e., the tubes and the detector do not revolve 360 degrees, but fewer, e.g. approximately 200.degree. --at least 180.degree., plus the aperture angle of the radiation cone. This problem is solved by an appropriate weighting of the measurement values (sinogram weighting).
2. Mechanical instabilities lead not only to deviations from the orbit for the focus path, but also to tilting of the detector. The optical axis generally no longer runs through the isocenter, for example. This necessitates two measures:
a) Determination of the "true" reception geometry (actual geometry). PA1 b) Consideration of the actual geometry in the back projection.
The determination of the reception geometry can be made with the aid of a marker ring, for example. If the fluctuations prove to be reproducible, then a tabulation of the geometry is possible by means of a calibration measurement.
The volume to be reconstructed is divided into discrete cubes--known as voxels (=volume element, in 2D: pixel=picture element). A voxel-driven back projection algorithm has the following form:
______________________________________ &gt;loop over all projections: &gt;determine position of projection center and detector &gt;loop over all voxels &gt;determine coordinates x,y,z of the voxel centerpoint &gt;determine the line from projection center through (x,y,z) &gt;determine the point of intersection of this line with the detector &gt;determine value to be back-projected &gt;back projection &gt;end voxel loop &gt;end projection loop ______________________________________
The 2D surface detector is likewise made discrete, e.g. through 1024 rows and 1024 columns. The connection line of a voxel with the projection center generally does not intersect a measurement value position, but an intermediate position. A bilinear interpolation between the four neighboring positions is common.
A central projection can be mathematically described by a 3.times.4 projective matrix P. This matrix is delivered by the position detection system. German OS 19 512 819 teaches the determination of the actual geometry with the aid of a marker ring. By the relationship b=P * r, an image point b of the 2D detector is allocated to each point r of the 3D space. Homogenous coordinates are used, i.e. r=(x,y,z,1) and b=(u, v, w)=w * (u/w, v/w, 1). The normalized coordinates u/w and v/w can be interpreted directly as row numbers and column numbers of the detector. The projective matrix P can be interpreted as product of two matrices: P=A[R, T], wherein, R is a 3.times.3 rotation matrix, T is a 3.times.1 translation vector, and A is a 3.times.3 upper triangle matrix containing the intrinsic parameters (camera, imaging relations, etc.). In order to determine the spatial position of focus and detector, this dismantling of P must be carried out. A method therefor is described in SPIE, Vol. 2708, pages 361 to 370. This resolution into intrinsic and extrinsic parameters has in practice proven to be a numerically unstable process. This means that the resulting translation vector T and the rotation matrix R, for example, can be subject to substantially greater errors than the original result matrix P of the position detection system.